Beyond Math by Sophia Magnusdottir

Sophia,

First let me say it was refreshing to review an alternative point of view regarding this discussion and yes I read your entire essay twice :).

Assume you're in a dark room and you accidentally spill hot coffee-you would naturally anticipate the liquid falling to the floor because you have been conditioned to expect this observation through experience, but nothing is natural about this occurrence. In fact this assumption is merely a good bias approximate expectation based on your previous experiences. The day you spill the coffee and it floats in front of you or it pours out like molasses, you will reconsider what is truth and how can you define it to predict reoccurring observations. The relevance of mathematics is not only to describe nature accurately (we could use easier methods) but it is to predict accurately past and future events without a bias conclusion. We study this field to become better at predicting and accurately describing events we observe. Without mathematics supporting the laws of physics we would random exist...and Mr(s). Pragmatic would not find common sense with anything observed.

Best Regards,

D.C. Adams

The difference between a conceptual based physics and a math based physics is the starting point. The conceive first method then describe mathematically to form measurements appeals to me. The difficulty is the math first approach (restate an equation then go look for it in nature) such as in quantum mechanics and transformation of General relativity are not conceptual. Today's physics is the latter. Perhaps the next great innovation will use the former method.

Dear Sophia,

What a refreshing essay. You have a delightful writing style that complements the clarity of your thinking.

I fully agree with your idea of analogs and duals that allow one to predict the behavior of the other. This is my model of consciousness, that is, our awareness of our brain modeling subsystems of the 'all'. Some, as you note, think of Friedmann's equations and their solution and they 'are' the model. I think of how classical spin works and then derive the theorem and the equations to describe the model. In this sense I think your thesis is right on target. I invite you to read my essay on the model I built first in my mind and then built a theory around. I believe modeling physics in your mind and then describing it mathematically is to be preferred to studying math and trying to guess what physics it describes. I believe that much math does not describe 'reality' in the same sense that much fantasy and fiction do not describe reality. Languages as maps are not restricted to real territory.

You've chosen a complex topic to write an essay on, as you note, almost blasphemy for some people. I think you did an excellent job presenting your ideas, and agree with them to the extent that I understand them correctly.

Thanks for contributing your essay, and good luck in the contest.

Edwin Eugene Klingman

Dear Pragmatic Physicist,

I think that perhaps we are related. My name is Practical Engineer. I enjoyed your essay quite a bit. I especially liked it when the time traveler was introduced to the Fire God.

Myself and my fellow tribesmen have been doing what you describe for a long time although we did not realize that it had any formalisms. We know that certain problems in heat transfer and fluid mechanics and mass transfer can be represented by certain forms of differential equations. We also know that certain electrical devices can be described by the same types of differential equations. None of us are very good with math, but my cousin Sparky can build those electrical boxes really good. So what we do is simplify the mathematical equations into common forms that use dimensionless numbers. My favorite is the Reynolds number but there are others like Nusselt and Prandtl. So cousin Sparky builds the box. Then we measure the voltage and the current at the different points of interest. Then we use the dimensionless groups to convert from volts and amps into mass and pressure or whatever we need to know.

The only problem is that it is a little expensive and slow. And if cousin Sparky makes a mistake then we have to start over.

There is another tribe on the other side of the mountain. We are on friendly terms with them. They aren't very good with math either. They made this thing they call a wind-tunnel. They claim to be able to fly. We think they're crazy.

Best Regards and Good Luck,

Gary Simpson

Physics without mathematics is like water without a cup.

Dear Sophia,

Your essay is near the top in quality of those that have appeared so far. Your topic sort of overlaps the last part of mine

http://fqxi.org/community/forum/topic/2320

I discuss largely the nature of mathematics I see shaping up that will be used by physics.

The reason that mathematics is used in physics is that we measure things and express that according to numbers. This of course goes way back with measuring weights, or distances and so forth. Physics of course has taken this to considerable extremes with measuring quantum eigenvalues and using measurements of scattering cross sections to back out quantum amplitudes and strengths of gauge interactions.

There are of course sciences that do not as heavily rely upon mathematics, such as biology. We have subjects such as psychology that have some small overlap with science, and this tends to reach a limit with sociology. Even these have some mathematics enter into their practice.

At the end you mention the linking of brains or minds, which will be facilitated with cybernetics. That might happen, and that will pave the way towards humanity becoming something other than it has been. We may become something completely different in the long run. This is of course assuming that we can survive far into the future. Under those conditions we can't know now what sorts of mental structures we will be thinking, or maybe groking or mind-melding, about.

Much of these alternatives you discuss are I think not demonstrable, or at least I see nothing either empirically possible or logically provable in order to support of verify one of these.

LC

Thanks for your essay Sophia. It is interesting and well written.

In the chapter "How to do science without mathematics", you explain that a computer might simply compare two subsets to find solutions without the need for a mathematical model. I might be wrong, but comparing two subsets is simple maths but it is still mathematics?

Hi Sophia,

I agree that the math approach is the easy approach. That's why current theoretical physics developments are conducted almost exclusively on a mathematical basis. However as you pointed out the math fist approach may not work. The math of super string theories requires eleven dimensions of space and time and there is no way to confirm the existence of these extra dimensions experimentally.

I have chosen the physics first approach and I was able to come up with a physical model of our universe called Model Mechanics. The different aspects of Model Mechanics can be used to replace the various abstract math objects (such as field/virtual particles, curvature in space-time dark energy, dark matter....etc.) in our current math theories.

I invite to read my essay and give me your informed comments. Thanks.

Regards,

Ken Seto

I agree, the pragmatic physicist does not have the right to risk knowledge advancement on ethical restraint, on social conventions, nor on philosophical disputation. Predictability is the dominant reality. This is not unlike Machiavelli for the world of true science. Use what works.

Hi. Interesting essay. Here are some thoughts about it:

You pointed out that when we need to approach or make predictions about processes from the world (subsystems of our universe), solutions ("models") can be developed not only in the form of mathematical theories but also as other processes from the world that somehow "behave the same". My opinion is that almost all processes in the world are so relatively complex and depending on many parameters (both physical constants and initial states of systems), that it would be extremely unlikely to discover 2 processes that behave the same (give the same result), except for a few very simple phenomena, or if they are made of the exact same stuff, or if one of them has been precisely well-designed for the purpose of matching the other. And I think only 2 kinds of systems (that you mentioned) are generally able to receive that needed amount of design for this purpose: well-programmed computers, and intelligent minds understanding a subject.

I mean, I don't believe in large usefulness for the other kind of "model" that you mentioned with the example of Analogue Gravity : they might provide vague similarities for specific processes but no full similarity, and cannot approach any accuracy I guess (sorry I did not check the article you gave as reference). For example, space-time outside the horizon of a black hole remains perfectly time-symmetric (if not distorted by a falling big mass); the time asymmetry only concerns what crosses the horizon. The acoustic model with a moving fluid does not show this fact, or at least does not make it intuitive. It can suggest some aspects but cannot be accurate because, well, moving fluids remain in a Galilean space-time and just cannot have a faithful correspondence with the curved space-time of General Relativity. Generally, digital computers can reproduce quite well any results that analogue models could provide (as any kind of analogue physical process can be described by known laws of physics, thus analyzed by these laws with methods of numerical analysis, except for quantum phenomena where classical computation would be inefficient, in which case making a quantum model, either "different stuff" quantum analog or by quantum computation, would be a hard problem anyway), with the advantage that they can be programmed to apply the exactly right law, while analog processes being subject to the specific laws ruling the stuff they are made of, are unlikely to behave the same as what we want.

Strictly speaking, computer simulations are mathematical stuff, even if they can look quite different from what is usually presented as "mathematics" at school. However, computer solutions can be considered largely non-mathematical when they heavily depend on the input of big data, which has a non-mathematical origin (see Jaron Lanier's talk on the myth of AI describing the situation of automatic translation systems).

Intelligent minds can also have both mathematical and non-mathematical abilities, that can be developed depending on needs. The advantage of mathematical abilities being their capacity of perfection to match a given rule, in case it would happen to be the right one; but I consider that only a mind can understand another mind, which is an ability beyond maths.

Now about your attempt at classifying views with sentences such as "Observations can be math", "Observations are described by math but are not math". I don't think such sentences make much sense. You don't seem to take them very seriously in the rest of your essay, but why did you develop them in the first place ? In particular, I doubt anyone would claim an observation "is math". An observation may be said to be "described by math" if some mathematical structures can be found there, in the sense that the observation is shown to not be entirely random. However I do not see it as a binary question "can be described or cannot be described by math", but rather a roughly continuous, quantitative question "how much can it be mathematically explained" in the sense of "compressed by some algorithm". So it is another sort of mathematical way of describing how mathematical something is, but it takes more subtle mathematical concepts than such basic set theory concepts as you did. See more explanations in my essay.